Robotic Multiphase Interaction: Manipulating Coupled Liquid and Solid Dynamics with a World Model

Yixuan Feng; Peng Wang

cs.ROSep 18, 2026

Robotic Multiphase Interaction: Manipulating Coupled Liquid and Solid Dynamics with a World Model

Authors: Yixuan Feng, Peng Wang

Organizations: College of Design and Engineering, National University of Singapore, 9 Engineering Dr 1, Singapore,117575. · Centre for Vision, Speech and Signal Processing (CVSSP), University of Surrey, Guildford GU2 7XH, United Kingdom.

Abstract

This work presents Robotic Multiphase Interaction (RMI), a setting in which liquid enters a porous material and interacts mechanically with its deforming solid skeleton. Manipulation can therefore change pore volume, expel or redistribute retained liquid, and alter grasp stability at the same time. Spilled liquid can also create safety risks in domestic and manufacturing settings. This differs from most manipulation of solid objects and from tasks that involve both liquid and solid while keeping the phases spatially separate. We study a sponge filled with water as the first RMI example. We use implicit incompressible porous flow with smoothed particle hydrodynamics as the dynamics engine and enable robotic manipulation by adding Coulomb contact memory, hybrid velocity and force regulation, and a stability gate for lifting. The resulting environment connects robot commands to changes in the coupled liquid and solid state. A world model conditioned on actions predicts how this state evolves under candidate commands, while a temporal UNet generates actions using either Diffusion Policy or rectified flow matching. Our world model reduces retained water prediction error by more than $60\%$ compared with the baseline. The best action sequence selected by the world model from policy proposals further reduces the predicted terminal water error by about half. These improvements show that modelling the coupled liquid and solid state helps the robot predict how its actions affect both the porous object and the liquid held inside.

Figures & tables

Fig. 1: Three manipulation settings. Left : conventional manipulation of a solid object, which may be rigid or deformable. Middle : both a solid and liquid are present but occupy different regions. Right : porous RMI, where liquid occupies the solid’s pore space and interacts with its deforming skeleton.

Fig. 2: RMI framework. Left : two grippers grasp a sponge soaked with liquid, with the relevant forces, contacts, and gripper width. $M^{S}$ and $M^{L}$ denote the solid and retained liquid masses, respectively. Middle : the state and action representations used in this work. Right : the training and inference pipeline for the world models and policies.

Fig. 3: Coulomb friction with contact memory. Each contacting solid particle stores an anchor in the gripper frame. The tangential displacement $\mathbf{e}_{s}$ and restoring demand $\mathbf{F}_{\mathrm{req},s}$ determine whether the contact sticks or slips within the Coulomb cone.

Interface	Model	Role
Causal	Baseline	The latest state through the rollout.
Causal	State-GRU-WM	Same GRU as AC-GRU-WM, no command.
Causal	AC-GRU-WM	Proposed world model, one command per step.
Lookahead	Linear-ARX	Locally linear residual on the full chunk.
Lookahead	AC-MLP-WM	One evaluation of $(\mathbf{y}_{t},\operatorname{vec}(\mathbf{A}_{t}))$ .

TABLE I: World model predictors. Causal models receive one command at each step, while lookahead models see the complete action chunk at once.

Fig. 4: One completed run for the medium sponge at

\phi=0.7

, using

210\,\mathrm{N}

to hold the sponge before lifting and

300\,\mathrm{N}

to squeeze it afterwards. The left axis shows target and measured gripper force, while the right axis shows retained water. Most liquid leaves as the measured force approaches the holding target. Lifting changes the retained water only modestly, and the later squeeze removes a smaller additional amount. Water is shown as a

2\,\mathrm{s}

trailing average.

Fig. 5: Water removed during each controller phase over all runs that reach that phase. The initial force ramp and hold dominate transport, while lifting has the smallest median effect. The post-ramp and post-hold phases constitute the later squeeze stage, which removes part of the remaining liquid. The distributions show that clamping and holding, rather than lifting, account for most transport through the porous material.

Fig. 6: Lift success over porosity and the force used to hold the sponge before lifting. Each cell combines the six later squeeze settings. All conditions with $\phi=0.5$ lift successfully. Higher porosity requires a stronger holding force and remains difficult for the small and large sponges.

Action input ablation
	$8\,\mathrm{cm}$			$10\,\mathrm{cm}$			$12\,\mathrm{cm}$
Method	water ( $\mathrm{g}$ )	force ( $\mathrm{N}$ )	fric.	water ( $\mathrm{g}$ )	force ( $\mathrm{N}$ )	fric.	water ( $\mathrm{g}$ )	force ( $\mathrm{N}$ )	fric.
Baseline	12.23	7.93	0.57	16.71	10.01	0.61	23.31	10.94	0.58
State-GRU-WM	9.42	9.62	0.61	9.02	6.77	0.65	17.03	12.98	0.68
AC-GRU-WM	4.32	3.78	0.72	6.59	4.74	0.79	17.53	11.04	0.61
AC-GRU-WM, shuffled $\mathbf{A}$	15.28	15.41	0.55	15.68	14.67	0.60	18.49	11.27	0.61

TABLE II: Causal world model prediction on the collected test split at

0.64\,\mathrm{s}

. We report water MAE in grams, force MAE in newtons, and balanced accuracy over four friction classes. The first three rows form the main comparison, and bold marks the best of these models. The final row is the action input ablation discussed in Sec. VI-B .

Method	$8\,\mathrm{cm}$ ( $\mathrm{g}$ )	$10\,\mathrm{cm}$ ( $\mathrm{g}$ )	$12\,\mathrm{cm}$ ( $\mathrm{g}$ )
Original controller action	2.56	4.23	4.68
Diffusion policy, first sample	2.79	4.30	4.94
Diffusion policy $+\ W_{\mathrm{T}}$	1.24	2.57	2.82
Flow matching, first sample	2.61	4.28	4.86
Flow matching $+\ W_{\mathrm{T}}$	1.11	2.24	2.45

TABLE III: Predicted terminal water error in grams for the original controller action, the first policy sample, and the action selected from eight samples by Transformer

W_{\mathrm{T}}

State	$8\,\mathrm{cm}$ ( $\mathrm{g}$ )	$10\,\mathrm{cm}$ ( $\mathrm{g}$ )	$12\,\mathrm{cm}$ ( $\mathrm{g}$ )
LS	9.11	10.85	8.41
LS $+$ G	8.68	11.70	14.63
LS $+$ G $+$ C	7.36	13.32	14.74
ALL	4.32	6.59	17.53

TABLE IV: Ablation of the state used by AC-GRU-WM at

0.64\,\mathrm{s}

, reported as water MAE in grams. LS contains liquid and solid phase variables, G adds gripper loading, C adds contact, and ALL adds residual slip.

Method	$8\,\mathrm{cm}$ ( $\mathrm{g\|N}$ )		$10\,\mathrm{cm}$ ( $\mathrm{g\|N}$ )		$12\,\mathrm{cm}$ ( $\mathrm{g\|N}$ )
	water	force	water	force	water	force
Linear-ARX	4.29	1.77	9.53	13.48	9.67	25.77
AC-MLP-WM	3.74	2.72	5.75	3.96	7.44	5.87
AC-MLP-WM, shuffled $\mathbf{A}$	17.47	13.41	26.15	19.60	42.87	26.02

TABLE V: Diagnostic in which the complete future action chunk is visible at every predicted step. Water and force MAE are reported at

0.64\,\mathrm{s}

in grams and newtons. Bold marks the best result within this diagnostic.

Method	$8\,\mathrm{cm}$ ( $\mathrm{N}$ )		$10\,\mathrm{cm}\,(\mathrm{N})$		$12\,\mathrm{cm}\,(\mathrm{N})$
	MAE F	smooth F	MAE F	smooth F	MAE F	smooth F
Diffusion policy	5.23	0.31	5.87	0.27	4.79	0.34
Flow matching	5.11	0.35	6.26	0.31	5.37	0.37

TABLE VI: Ablation of the policy training objective on a shared temporal UNet. We report force MAE and the mean force change per step for one sample, with both quantities measured in newtons. Each sponge size contributes several thousand test windows.

Action source	$8\,\mathrm{cm}$	$10\,\mathrm{cm}$	$12\,\mathrm{cm}$
Original controller action	3.61	5.22	6.00
DP-UNet $+\ W_{\mathrm{T}}$	2.61	3.69	4.37
FM-UNet $+\ W_{\mathrm{T}}$	2.51	3.43	4.06

TABLE S1: Combined predicted cost

J

for the original and selected actions.

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Abstract

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